JEE Advanced2008MathematicsPermutation and CombinationActual
Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.
Options
- A(A) r, (B) q, (C) s, (D) p
- B(A) p, (B) s, (C) q, (D) q
- C(A) p, (B) r, (C) s, (D) q
- D(A) r, (B) s, (C) r, (D) p
Correct answer
B. (A) p, (B) s, (C) q, (D) q
Step-by-step solution
(A) If ENDEA is fixed word, then assume this as a single letter. Total number of letters =5 and total number of arrangements =5 ! . (B) If E is at first and last places, then total number of permutations 7 ! 2 ! =21 5 ! (C) If D , L , N are not in last five positions D , L , N , N E, E, E, A, O Total number of permutations = 4 ! 2 ! 5 ! 3 ! =2 5 ! . (D) Total number of odd positions =5 Permutations of AEEEO are 5 ! 3 ! Total number of even positions =4 Number of permutations of N , N , D , L = 4 ! 2 ! Hence, total